The present invention relates to quantum electronic circuits for applications to quantum information processing and more specifically to systems and methods for implementing and operating such devices by embedding a superconducting circuit within a waveguide-beyond-cutoff (WBC).
An electronic quantum circuit for quantum information processing must be sufficiently isolated from the electromagnetic (EM) environment that its quantum coherence can persist a useful length of time, yet still interact with the external world so it can be controlled and measured. The physical sizes and coupling strengths typically realized in superconducting quantum circuit devices favor strong interactions with the external environment over isolation, so they tend towards being straightforward to control and measure but difficult to isolate from uncontrolled degrees of freedom in the surrounding EM environment. Several methods have previously been developed to enhance the attainable degree of isolation of the quantum degree of freedom of interest, such as exploiting symmetries in the circuit Hamiltonian and engineering the eigenstate energy spectrum with respect to charge and flux.
A quantum electronic circuit having a transition frequency ω loses energy to the environment, described by an admittance Y(ω), at the rate:κq=1/T1(ω)=Re[Y(ω)]/Cq  (Eq. 1)where Y(ω) is the admittance as seen by the mode of the quantum circuit at frequency ω; T1 is the energy decay time, and Cq is the characteristic capacitance of the mode. One important objective in the design and development of quantum circuits for applications to quantum information processing is the minimization of this relaxation rate. One tool for doing this involves coupling the non-linear quantum circuit (qubit) to the environment through a linear resonator. This approach, called circuit Quantum Electrodynamics, or circuit QED, has emerged over the past decade to become the standard paradigm for the design and operation of superconducting quantum circuits. The filtering action of the environment impedance facilitates longer coherence at frequencies sufficiently far from the resonator frequency. It also favors more stable device operation, as fluctuations of the environment modes are also filtered. Further, the linear resonance mode acts as a mechanism to allow projective quantum measurement of the state of the non-linear circuit.
In the circuit QED geometry, the qubit may still lose energy to the environment via off-resonant or dispersive energy relaxation via the resonator mode, a process referred to as Purcell effect relaxation. The limit on quantum circuit relaxation rates presented by this effect is set by the quantum circuit frequency and the degree of anharmonicity of its energy level spectrum; the resonator frequencies (including possible spurious higher modes), and the couplings between them.
In circuit QED measurement of the qubit state is accomplished by exploiting the coupling between the qubit and the resonator: excitations of the qubit induce a qubit-state-dependent pull of the cavity frequency. The inverse effect, where, cavity photon number fluctuations pull the qubit frequency, leads to a dephasing process of the qubit that can suppress qubit phase coherence time T2 below the limit of 2T1 set by energy relaxation. Minimizing this and other pure dephasing mechanisms is a second design goal for superconducting quantum circuits.